capacity of a single runway

Maximum Throughput Capacity

Capacity of a Single RunwayKimberly Afcha and Danielle Hettmann Measure of capacity of the runwayBased on the following assumptions: Continuous supply of arrivals and/or departuresAir Traffic Control rule no simultaneous Runway Occupancy (SRO)Air Traffic Control rule safe Wake Vortex Separation Distances between two flights Static fleet mixApproach procedure does not changeMaximum Throughput Capacity (MCT)

This video will discuss maximum throughput capacity or MCT. MCT is a measure of the capacity of the runway. It defines the average number of arrivals and/or departures that can be performed on the runway in one hour.

MCT makes several assumptions, that are listed on the screen. Because of these assumptions, MCT is a theoretical measure of capacity and is represented as an average capacity for the runway.

The following sections will describe a method for estimating MCT on a runway for arriving aircraft. 2Five considerations: 1. ATC Safety Rule: no Simultaneous Runway Occupancy (SRO)2. ATC Safety Rule: Maintain Wake Vortex Separation Distance between lead and follow aircraft3. ATC Controller/Pilot Separation Control Accuracy: ATC/Pilots insert a buffer distance to avoid violating separation rules4. Fleet Mix: determines the type of aircraft in the lead-follow pairs. The type of aircraft determines the separation distance used. Small aircraft following large aircraft require longer distances than large aircraft following large aircraft.5. Final Approach Path Distance: the length of time lead-follow aircraft fly the approach in pairs and separationMCT of a Runway

When determining the MCT of a runway, there are five things to consider. ATC safety rule dictates there be no simultaneous runway occupancy. ATC safety rule dictates there be a wake vortex seperation distance between leading and following aircraftATC and pilots must insert a buffer distance in order to maintain separation rules. Fleet mix must be considered. Small aircraft following large aircraft require longer distances than large aircraft following large aircraft. The buffer spacing required for compression and separation is determined by the length of time the lead-follow aircraft fly the approach. 3Modeling MCT

This table includes important equations for determining MCT with no SRO, wake vortex separation rule, and the controller/pilot separation buffer.

Column three includes equations for homogeneous fleet mix while column four includes equations for non-homogeneous fleet mix. We will revisit theses equations in detail. 4Maximum Throughput Capacity for a Homogeneous Fleet Mix

Simultaneous Runway Occupancy (SRO): MCT = 3600 seconds/ROTWake Vortex Separation DistanceDetermined by separation distanceWake vortices generated off wing-tips of aircraftStrength of the vortex is governed by the weight, speed, and shape of the wing of the generating aircraftMCT for Homogeneous Fleet Mix

When concerned only with the SRO rule, MCT is 3600 seconds divided by ROT. ROT ranges from 45 seconds for small aircraft to 70 seconds for large aircraft. For example, the MCT for a homogeneous fleet with ROT of 60 seconds, the MCT would be 60 flights/hour.

Wake Vortex Turbulenceis defined as turbulence which is generated by the passage of an aircraft in flight. Air spills over the edge of the wings creating two tubes of air that trail behind the aircraft. Disturbances from air friction and air turbulence cause the wake to sink and dissipate. A typical wake will sink approximately 800 feel from the point of origin and will exist at this point for about 90 seconds. 6MCT = 3600 / (s/v) where t = s/vt = inter-arrival times = distance between aircraft at runway thresholdv = groundspeed of aircraftExample: Heavy following Heavy, t=96 secondsMCT = 36000 / 96 = 37.5 flights/hour

Minimum Separation Distance

To combat the potential effects of wake vortices, ATC are required to maintain separation between aircraft based on an established minimum separation distance. The larger the lead aircraft and the smaller the follow aircraft, the larger the distances required as the lead aircraft crosses the runway threshold.

MCT (meeting the wake vortex separation rule and homogeneous fleet mix rules) is determined by the inter-arrival time (t), based on the distance between aircraft at the runway threshold (s) and the groundspeed of the aircraft (v). Using this equation for a heavy following heavy aircraft, the MCT is 37.5 flights/hour, which is more restrictive than the 60 flights/hour determined through runway occupancy time.

7Separation distance is determined through coordination of ATC and pilotSeparation Buffer: MCT = 3600 / ((s/v)+b)t = inter-arrival times = distance between aircraft at runway thresholdv = groundspeed of aircraftb = bufferExample: Heavy following Heavy, t=96 secondsMCT = 36000 / (96 + 10)= 34 flights/hour

ATC/Controller Separation Buffer

Collaboration between the ATC and pilot held determine separation distance. The controller uses radar to track the aircraft and provide instructions to the pilot of the leading aircraft to speed-up or slow-down. The pilots monitor the aircraft in front of them and follow controller instructions. In the United States, the average separation distances exceed the minimum separation distances by a buffer of 10 to 25 seconds as controllers tend to be conservative and create larger separation distances.

Using the MCT equation for a heavy following heavy aircraft, an additional 10 seconds of buffer yields an inter-arrival time of 106 seconds and produces an MCT of 34 flights/hour.

8MCT = Min(MCTSRO, MCTWVSD, MCTWVSDB)SRO = Single Runway OccupancyWVSD = Wake Vortex Separation DistanceWVSDB = Wake Vortex Separation Distance and Buffer (ATC/Controller Buffer)

Simplified to:

MCT = Min(MCTSRO, MCTWVSDB)

MCT for a Homogeneous Fleet Mix

Maximum Throughput Capacity is the minimum capacity throughput for the SRO, wake vortex, and ATC/controller buffer values. Since ATC/Controller Buffer increases the inter-arrival time, the equation for MCT can be simplified to the minimum capacity throughput for the SRO and ATC/Controller Buffer.

9Maximum Throughput Capacity for a Non-Homogeneous Fleet Mix

MTC-Non Homogenous Fleet MixMTC = Min ( MTCSRO, MTCWVSDB)Fleet MixProbability of Type of AircraftH.3L.2M.25S.25

When dealing with a non-homogenous fleet mix, we take into account the probabilities of each type of aircraft. For the remainder of the presentation the following numbers will be used. These numbers can be plugged in to the probability column of the Runway Capacity Spreadsheet.

Once again, when computing the Maximum Throughput Capacity for a non homogenous fleet mix we follow the simplified version of the equation for MTC; Basically, finding the Minimum of MTC following only the Simultaneous Runway Occupancy rule, and MTC following only the wake vortex separation distance with a buffer distance rule.

Next, we will discuss how to compute both of these MT capacities for a non homogenous fleet mix. 11Runway Occupancy Time (ROT)

Probability of lead-follow

MTC- Simultaneous Runway Occupancy Rule

When computing Max Through Cap following only the SRO rule, we will take two things into considerationFirst, the runway occupancy time and Second, the probability of the lead-follow.

With these two items into consideration we can compute the expected Runway Occupancy Time12Computing E[ROT]

E[ROT] = i (pi * ROTi)E[ROT] = (.3*80) + (.2*65) + (.25*50) + (.25* 45) = 60.75

We do this by adding the probability of the lead aircraft, i, times the runway occupancy time for the lead aircraft, i. The numbers presented will be used as an example and can be inserted to the occupancy column in the Runway capacity Spreadsheet. With these numbers, the expected Runway occupancy time for our mix fleet is .3 * 80 plus.Our expected value is 60.75.

13MTCSRO= 3600/ E[ROT]

MTCSRO= 3600/60.75 = 59.26

MTC-Simultaneous Runway Occupancy Rule

Once we have the expected value, thee MCT following only the SRO rule is defined as

3600/ Expected [ROT], in our example that would be 3600 divided by 60.75Which yields a MTC of 59.26.

14The separation distance between the lead and the follow (sij)The groundspeed of the aircraft (vj)The probability of a lead-follow pair (pij)

MTC-Wake Vortex Separation Rule

Now, when computing the MTC following only the Wake Vortex Separation Rule, we take into consideration 1. The separation distance between the lead and the follow (sij)2. The groundspeed of the aircraft (vj)And 3. The probability of a lead-follow pair (pij)

15Inter-arrival time (tij)Inter-arrvial time matrix T

E[Tij] = ij (pij *( Tij))


Before computing the MTC following only the Wake Vortex Separation Rule, we need to define the time between the lead and the follow aircraft as the inter-arrival time (tij)

The Interarrival time for all possible pairs, is represented by a inter-arrival time matrix T like the one showing

As you might expect, each cell represents the inter-arrival time for a given pair. Each cell is computed by adding up the probability of a given pair times the appropriate inter-arrival time for that pair, for all possible pairs. Note that pij is computed by multiplying the probability of leadtimes the probability of follow

We will now discuss how to compute Tij

16Tij = sij/vj for compression caseTij = ((r + sij)/vj ) (r/ vi ) for separation case


Tij will be defined as the separation distance between Lead and Follow over the groundspeed of Follow for a compression case

And defined as the length of the approach path plus the separation distance between lead and follow over the groundspeed of follow minus the approach path over the groundspeed of Lead for a separation case.

There are 2 equations to compute Tij for the compression and separation case17Lead slower than Follow

Compression distance- additional distance used by Follow as it catches up to Lead

Compression Time = r/(Vj Vi)

Cases: H-H, H-L, H-M, H-S, L-L, L-M, L-S, M-M, M-S, S-SCompression Case

We face compression case when the Lead is slower than the Follow. In order to ensure the separation distance is maintained, the Follow aircraft is separated by the required separation distance plus an additional compression distance.

This distance represented as time is difined as the length of the approach path divided by the relative groundspeed between lead and follow aircraft18Lead faster than Follow

Separation Distance- additional distance at the runway threshold caused by Lead faster than FollowSeparation Time= ((r + sij)/vj ) (r/ vi )

Cases: S-M, S-L, SH, M-L, M-H, H-L.Separation Case

Now, we face a separation case when the lead aircraft is faster than the follow aircraft. Once again in order to ensure the separation distance is kept, the follow aircraft is separated from the lead according to the required separation distance at the start of the approach.

The separation distance represented as a time is defined by the equation shown. 19MTC = 3600 seconds/E[tij]

E[tij]= (.09*120)+(.06*188)++(.06*120) =141.9

MCT = 3600 seconds/141.9 = 25.368


Now that the Expected inter-arrival time has been computed we can go ahead and plug it in into the MTC formula shown. The result given the numbers provided into our example lead to an MTC of 25. 368 arrivals per hour.

The same computation can be obtained from the Runway capacity spreadsheet when plugging in the required distance separation between aircraft pairs into the appropriate table in the spreadsheet. 20MTC = 3600/E[tij]Where tij = Tij + b

E[tij]= 146.9 secondsMTC= 3600/ 146.9 = 24.505 arrivals per hour

MTC-Wake Vortex Separation Rule with Buffer Distance

When dealing with the MTC following only the Wake Vortex Separation Rule with a Buffer distance, we follow the same MTC formula with a minor adjustment computing the expected inter-arrival time.

Now, the interarrival time takes into consideration the buffer distance. In our example it is set to be 5 seconds. The buffer distance in time can be plugged in, in the appropriate cell (D11) in the runway capacity spreadsheet. With the 5 second buffer distance, we Yield a MTC of 24.505 arrivals per hour.

21Recall

MTC = Min ( MTCSRO, MTCWVSDB)

MTC = Min (59.26, 24.505) = 24.505 arrivals per hour

MTC-Non Homogenous Fleet Mix

Now, in order to compute the MTC for a non homogenous fleet mix,

Recall that we need to find the minimum between the MTC following the SRO rule and MTC following the WVS with a distance buffer.

In this case, the MTC for a non homogenous flee mix is 24.505 arrivals per hour.

22Runway Arrival CapacityEnter Inforfmation HereCoded by L. Sherry from deNeufville/Odoni, 2003, pg 408). Modified Classes, Separation Distances, added Passengers.Aircraft Speed, Runway Occupancy TimeIpspeedoDefault p(a/c type)(prob.)(mph)(sec)I(H)0.3150800.260.752(L)0.2130650.3559.259259259333.96226415093(M)0.25110500.354(S)0.2590450.1Must Equal Zero1Length ofATC Buffer TimeApproach Path0secs6milesRequired Distance Seperations (mi) (given)Trailing aircraftleading1(H)2(L)3(M)4(S)aircraftI(H)56782(L)2223S =3(M)22244(S)3333Results (DO NOT ADJUST CELLS)Inter-Arrival Time (sec)Time Seperation (mins)Trailing aircraftTrailing aircraftleading1(H)2(L)3(M)4(S)leading1(H)2(L)3(M)4(S)aircraftI(H)120188281416aircraftI(H)2.003.144.696.932(L)6565961942(L)1.081.081.593.23T =3(M)505565204T =3(M)0.830.921.093.394(S)7283981204(S)1.201.381.642.00Probability of Leading/Trailing PairsTrailing aircraftleading1(H)2(L)3(M)4(S)aircraftI(H)0.090.060.080.082(L)0.060.040.050.05P =3(M)0.080.050.060.064(S)0.080.050.060.06Tij x PijLeadTrailTotal AircraftPassengers per Aircraft ClassH10.811.321.131.274.4524L3.92.64.89.721.0304M3.82.84.112.723.3106S5.44.26.17.523.294141.91028Expected time seperation141.9secAverage runway capacity25.368arrivals/hr

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capacity of a single runway

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